Kitten poops, but will not pee in litter box!

So I found a stray kitten outside where I work, underneath a pallet, in the hot sun crying. He had been there for a couple days before I was able to catch him, so I'm pretty sure mom was gone. I couldn't leave him there since he was so tiny and weak, so I brought him home. I took him to the vet the next day, and found out that he is about 6 weeks old and other then being a little skinny, he got a clean bill of health. He didn't even have fleas!

I have 3 adult indoor cats already, so my intention is just to foster him until I can get him neutered, then find him a home. For the first couple days (I found him Tuesday) I confined him to a small bathroom, where he was using the litter box perfectly for both pees and poops. I gradually started letting him out into the rest of my apartment to get him socialized and used to other people/animals. He will poop in the litter box no problem, but he will NOT pee in it on his own when he is anywhere other then my small bathroom. He seems to like anything that feels like carpet, so while I have a tile floor, both my cat towers, the couch and all rugs are fair game. I have been able to catch him before he pees most of the time and put him in his litter box, cause I see him start to squat, but other times I can't, cause he will be playing one second, and then squatting to pee the next where ever he happens to be. He is a fast little bugger too!

My other big problem is that I live on a small island, so finding enzymatic cleaners or cat attract litter or anything like that is pretty much impossible. I have been using vinegar and peroxide/baking soda to try to eliminate the odors, but he just keeps doing it. Every time I think he might be getting the hang of it, he has another accident. Does anyone have any basic solutions that I can try? I am reduced to having to keep him in the bathroom most of the time, but I feel terrible because he just cries and cries now since he wants to be out with everyone else, as he has made friends with my other 3 cats.

Since he is only 6 weeks old, it's going to be awhile before I can get him neutered and re-homed, so I really need to figure something out with his litter box issues soon. I can't have him peeing everywhere, or I fear my other cats will follow suit... 

First thought I had was more litter boxes for two reasons...

1. He's a little guy and has a small bladder

2. Some cats will not pee and poop in the same litter box

I would recommend that he have his own kitten-sized litter pan, and that you leave it in the bathroom for him to use there, but do not close him up in the bathroom. Allow him to come and go, but make sure he knows "his" pan is in there.

I agree that confining him to the bathroom is not good for him socially. He's at a tender age and needs to interact with your other cats.

I hope he'll begin peeing in his pan again if it's in the bathroom. Thank you for caring for this little guy!

He has 3 litter boxes available. I thought he was doing really well, no accident for over a day. But he's just peed on my bed... And I had put him in the litter box not even 5 minutes before to check. 

It sounds like he's trying though. Let's hope he gets better and better at at. At 6 weeks old he is right in the learning curve. My kittens learned around that age, but one had accidents and took longer than the others.

I am being patient with him, of course. He is so darn cute, it's really hard to be mad. And I can see the gratefulness in his eyes. I'm hopeful that he will catch on soon. I was moving "his" litter box from the bathroom to the living room when I let him out, but I will try leaving it in the bathroom. Maybe he is searching for it when I'm not looking and missing it. 

Moving the litter box around is a problem.  He may not be able to find it or remember where it is.  You need a small one in each room he goes to for now.  Small kittens have small bladders.  And short memories I hear.   As he gets bigger, you can take some away.

That makes a lot of sense. I will go get a couple more boxes tomorrow. I always remember kittens kind of getting it right away, so this one threw me. Now I feel bad that it's probably me that is confusing him!